Assessed Task(s):

Set and Venn Diagram Unit Test (Criterion A)

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Objectives:

Use set language and notation, and Venn diagrams to describe sets and represent relationships between sets as follows:

Understand and use the following notation:

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As an IB Learner you are reflective. On your own page of your blog you will need to explain each of these important ideas in your own words:

1. Denoting Sets

2. Sets of Numbers

3. Universal and Empty Sets

4. Equal and Equivalent Sets

5. Venn Diagrams

6. Operations with sets

7. Cardinality of unions and intersections.

8. De Morgan's laws

9. Survey problems

10. One-to-one correspondence

11. Fundamental counting principle

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TYPES OF PROBLEMS YOU WILL NEED TO SOLVE:

• Tell whether a set is well defined.

• Specify sets by roster and by description.

• Understand and use set-builder notation.

• Draw Venn diagrams showing subsets, equal sets, or disjoint sets.

• Distinguish between equal and equivalent sets, and find the cardinality of a given set.

• Distinguish the symbols for subset, proper subset, and element.

• Find the complement of a set.

• Find the union of two sets.

• Find the intersection of two sets.

• Recognize and draw the Venn diagrams for union, intersection, and complement.

• Solve survey problems involving two sets.

• Perform mixed operations using union, intersection, and complement

• Draw Venn diagrams for mixed operations using union, intersection, and complement.

• Draw Venn diagrams using three or more sets.

• Prove or disprove set statements using Venn diagrams.

• Solve survey problems involving three or more sets.

• Find the Cartesian product of two sets, and determine its cardinality.

• Find the cardinality of a given set.

• Determine whether sets have the same cardinality by placing them in a one-to-one correspondence.

• Classify a given set at finite or infinite.

• Show that a given set has cardinality aleph null.

• Show that a given set is infinite.

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Sets, Subsets & Venn Diagrams

Video:

Venn Diagrams (2:00)

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Georg Cantor:
http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Cantor.html

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John Venn:
http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Venn.html

Reference Topic Sites:

This is a general review of the material of this section.
http://library.thinkquest.org/C0126820/setsubset.html

This site is a general introduction to sets.
http://www.math.uncc.edu/~droyster/math3181/notes/hyprgeom/node8.html

Basic concepts and notation for sets:
http://www.math.utah.edu/~alfeld/math/sets.html

This site reviews sets and set notation:
http://www.math.csusb.edu/notes/sets/node1.html#SECTION00010000000000000000

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Operations with Sets

Reference Topic Sites:

This is a web-based instructional module on the algebra of sets.
http://lrs.ed.uiuc.edu/students/avilesga/project/main.html

Union of Sets:
http://lrs.ed.uiuc.edu/students/avilesga/project/union.html

Intersection of Sets:
http://lrs.ed.uiuc.edu/students/avilesga/project/intersection.html

Venn Diagrams for union and intersection:
http://lrs.ed.uiuc.edu/students/avilesga/project/venn.html

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Applications of Sets

Reference Topic Sites:

This site gives some interesting practice with combined operations with sets:
http://ww2.unime.it/dipart/i_fismed/wbt/mirror/moe/tests/mengen/duv.html

Venn diagrams with two, three, and four sets:
If you click on the question mark, you can practice with three overlapping sets.
http://www.math.csusb.edu/notes/sets/node5.html

This site shows a statement of De Morgan's law.
http://www.demorgan.com/demorgan.htm

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Finite and Infinite Sets

Video:

Infinity. (time: 9:42)
The smallest Infinity (time: 9:33)

Reference Topic Sites:

This site introduces the idea of infinite sets:
http://mathforum.org/isaac/problems/cantor1.html

This site introduces the idea that there are different sizes of infinity:
http:http://personal.bgsu.edu/~carother/infinite/Infinite1.html

"A Crash course in the Mathematics of Infinite Sets," by Peter Suber, Earlham College:
http://www.earlham.edu/~peters/writing/infapp.htm

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